People have long been fascinated, entertained, and enlightened by logic-based puzzles. The enormous variety of such puzzles may provide delight to both children and adults. Though a number of factors relate to the enjoyability of a particular logic-based puzzle for a particular person, the level of complexity, the configurability of the pieces, and the presence of colors, symbols, and/or sounds may all contribute.
Further, apart from their use as devices for entertainment, logic-based puzzles may be used to test the spatial reasoning or logic of individuals. Studies have confirmed that analytical thought of the type elicited by such logic-based puzzles can improve one's capacity for learning and recalling information. Such tests may help determine individuals suited for a particular task, or train individuals for a particular task. For example, individuals who are candidates to be astronauts need to have a tremendous aptitude for spatial reasoning. This is because much of a routine, Earth-based analysis of various objects is based on an individual's relationship to those objects, as determined by one or more points of reference (such as the Earth's gravity). However, in space, many of these variables (e.g., gravity, or other points of reference) may not exist. Thus, the ability of an individual to understand the orientation of various objects when no standard point of reference exists can be critical.
Of the many types of logic-based puzzles, one example that is known is a 4×4 square grid having fifteen slidable tiles numbered 1-15 occupying fifteen of the sixteen spaces within the grid. Tiles can be slid sequentially into the empty space in the grid, thereby altering the relative positions of the numbered tiles. The typical solution to such a puzzle is obtained when the tiles are numerically ordered 1-15 reading left-to-right across the columns and then down the rows, for example.
Another well-known logic-based puzzle is the Rubik's Cube®. This cube-shaped puzzle has six faces each including a 3×3 grid of nine colored stickers. The stickers adhere to 26 plastic pieces emanating radially from a central core. The various perpendicular planes of eight or nine pieces are rotatable about the central core to reconfigure the cube and the arrangement of stickers thereon. The typical solution to this puzzle is obtained when all nine stickers on each face are of identical color and each of the six faces of the cube has stickers of a different color from each of the other five faces.
These and many other logic-based puzzles use recognizable patterns of colors, letters, numbers, and the like to distinguish a “solution state” from a “non-solution state.” Such puzzles can be used to challenge the player's ability to form and remember spatial relationships in three dimensions. However, in each of the puzzles described above, the player can observe all of the puzzle pieces, or all sides of the cube at once, before deciding on a next “move” to make. In other words, many present puzzles allow the user to see alternative sides of the puzzle pieces by rotating the entire puzzle. They do not require the individual to remember the spatial relationship among the faces of the object, in three-dimensional space. Thus, they cannot be used to ultimately test all spatial reasoning abilities. Thus, a puzzle that allows for such testing of an individual would be desirable.